Will the EC50 be different if all Y values are converted to logs before fitting a log(dose) response curve?  

Converting Y values to logarithms will definitely change the meaning and value of the EC₅₀.

The EC₅₀ is the concentration that provokes a response (Y) half-way between the bottom and top plateaus. Imagine that the response ranges from 1 to 1000. Half-way between is 500.5, so the EC₅₀ is the X value (concentration) that provokes a response of 500.5. Now transform the Y values to logarithms (base 10). The response, on a log scale, now ranges from 0 to 3. Half-way between is 1.5, so the EC₅₀ is the concentration that provokes a response whose log is 1.5. That means the response itself, the antilog of 1.5, is 31.6. So the "EC₅₀" changes from the value needed to provoke a response of about 500 to one that provokes a response of about 30, simply by converting Y values to logs.

Should the Y values be transformed? There are two considerations.

• The EC50, unlike rate constants and equilibrium constants, is not a parameter in any molecular model. Rather, it simply describes a dose-response curve. Change the definition of response, and you'll change the EC50. Which is most 'correct' depends on the scientific context, and the traditions in your particular scientific niche.
• Nonlinear regression is based on the assumption that the scatter among replicates is Gaussian. Transforming Y values to make the scatter among replicates more Gaussian  ensures that the curve fitting results are interpretable.